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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — Answers

Answer sheet with worked solutions for the Year 8 linear relationships & graphs worksheet.

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Year 8 Gradient and Linear Equations Worksheet — Level 3 — Practice Set 4 — Answers

Show your working. Gradient = rise ÷ run; the equation of a line can be written as y = (gradient)x + (y-intercept).

1.For the line y = −6x − 7, write the gradient and the y-intercept.

Answer: gradient −6; y-intercept −7

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

2.Does the point (−2, 0) lie on the line y = 4x + 8?
  1. AYes
  2. BNo

Answer: Yes

Substitute x = −2: y = 4 × (−2) + 8 = 0, which matches.

3.Does the point (3, 6) lie on the line y = 4x − 7?
  1. AYes
  2. BNo

Answer: No

Substitute x = 3: y = 4 × 3 − 7 = 5, not 6.

4.For the line y = −6x + 8, write the gradient and the y-intercept.

Answer: gradient −6; y-intercept 8

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

5.Does the point (−2, −7) lie on the line y = 3x − 4?
  1. AYes
  2. BNo

Answer: No

Substitute x = −2: y = 3 × (−2) − 4 = −10, not −7.

6.For the line y = 5x − 9, write the gradient and the y-intercept.

Answer: gradient 5; y-intercept −9

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

7.Does the point (4, −7) lie on the line y = −3x + 8?
  1. AYes
  2. BNo

Answer: No

Substitute x = 4: y = −3 × 4 + 8 = −4, not −7.

8.For the line y = 6x − 8, write the gradient and the y-intercept.

Answer: gradient 6; y-intercept −8

In y = (gradient)x + (y-intercept), the number multiplying x is the gradient and the constant is where the line crosses the y-axis.

9.A line has a gradient of −1 and passes through (3, 4). Find its equation.

Answer: y = −x + 7

  1. y = −1x + (y-intercept)
  2. 4 = −1 × 3 + (y-intercept)
  3. y-intercept = 4 − (−3) = 7
  4. y = −x + 7
10.A line has a gradient of −5 and passes through (−4, 24). Find its equation.

Answer: y = −5x + 4

  1. y = −5x + (y-intercept)
  2. 24 = −5 × (−4) + (y-intercept)
  3. y-intercept = 24 − 20 = 4
  4. y = −5x + 4
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